
Due to the identity \(\mathbf {vec}(\mathbf {A}\mathbf {B}\mathbf {C}) = (\mathbf {C}^\top \otimes \mathbf {A})\mathbf {vec}(\mathbf {B})\)  [1]}, we can write this as
\(p_{SA}^* &= \max _{\mathbf {V}_i} -\sum _{i=1}^n \mathcal {L}^*\left(\mathbf {V}_i, \mathbf {Y}_i\right) \nonumber \\\mathrm {s.t.}~& \max _{\Vert \mathbf {w}_{1}\Vert _2 \le 1} \left\Vert \sum _{i=1}^n ( ({\mathbf {X}}_i^\top \otimes \mathbf {V}_i^\top )({\mathbf {X}}_i \otimes {\mathbf {X}}_i)) \mathbf {w}_{1} \right\Vert _2 \le \beta ,\) 
